Implementing collection of sets with trie: a stepping stone for performances ?

Main operations of the Set Collection Abstract Data Type are insertion, research and deletion. A well known option to implement these operations is to use hashtable. Although hashtable does not admit good time complexities in the worst case, the practical time complexities are efficient. Another option is to use the data structure known as the trie. The trie is useful for two main reasons. Firstly, with such a data structure, mentionned operations admit very good theoretical time complexities. Secondly a trie can be seen as a compact representation of a collection of sets since some parts of them are merged together. Aim of this article is to evaluate performances of the trie data structure. The Java language proposes an abstract class corresponding to the Set Collection A.D.T. operations. We propose in this article three different implementations of this abstract class. All of them are variations of the way to manage the sons of nodes. Theoretical complexities are then evaluated. After that, comparison with performances of hashtable are made in different contexts depending of the collection density, the set size and the ground set size. Finally we analyze our results and conclude in which cases the trie structure outperforms others structures

A new generic class of Frankl’s families

Frankl’s conjecture states that in a family of sets closed by union F such that F 6= {∅}, there is an element that belongs to at least half of the sets of F. There are several partial results of this conjecture. For example, it has been shown that families in which the smallest set is of size 1 or 2, or families closed both by union and by intersection are Frankl’s. In this article, by basing ourselves on an unseen recursive definition of the family of sets closed by union, we will define a new class of Frankl’s families. Subsequently, we will evaluate the size of this class for the first 6 values of n. Finally we will show that this class does not coincide with the already known Frankl’s classes

Adenine methylation is very scarce in the Drosophila genome and not erased by the ten-eleven translocation dioxygenase

N6-methyladenine (6mA) DNA modification has recently been described in metazoans, including in Drosophila, for which the erasure of this epigenetic mark has been ascribed to the ten-eleven translocation (TET) enzyme. Here, we re-evaluated 6mA presence and TET impact on the Drosophila genome. Using axenic or conventional breeding conditions, we found traces of 6mA by LC-MS/MS and no significant increase in 6mA levels in the absence of TET, suggesting that this modification is present at very low levels in the Drosophila genome but not regulated by TET. Consistent with this latter hypothesis, further molecular and genetic analyses showed that TET does not demethylate 6mA but acts essentially in an enzymatic-independent manner. Our results call for further caution concerning the role and regulation of 6mA DNA modification in metazoans and underline the importance of TET non-enzymatic activity for fly development

Drosophila TET acts with PRC1 to activate gene expression independently of its catalytic activity

Enzymes of the ten-eleven translocation (TET) family play a key role in the regulation of gene expression by oxidizing 5-methylcytosine (5mC), a prominent epigenetic mark in many species. Yet, TET proteins also have less characterized noncanonical modes of action, notably in Drosophila, whose genome is devoid of 5mC. Here, we show that Drosophila TET activates the expression of genes required for larval central nervous system (CNS) development mainly in a catalytic-independent manner. Genome-wide profiling shows that TET is recruited to enhancer and promoter regions bound by Polycomb group complex (PcG) proteins. We found that TET interacts and colocalizes on chromatin preferentially with Polycomb repressor complex 1 (PRC1) rather than PRC2. Furthermore, PRC1 but not PRC2 is required for the activation of TET target genes. Last, our results suggest that TET and PRC1 binding to activated genes is interdependent. These data highlight the importance of TET noncatalytic function and the role of PRC1 for gene activation in the Drosophila larval CNS

Quelques aspects algorithmiques sur les systèmes de fermeture

This thesis deals with some algorithmic aspects on closure systems and their different representations. We present different definitions and notations on closure systems and the link between closure systems and Horn theories, we are interrested in three operations on closure systems: join, meet and difference. This thesis propose a characterization on this operation with respect to representation of closure systems we consider. We translate results of equivalent problems studied on Horn theory and give some new contributions. Then, we deal with generation of a mixte implicational basis of a formal context. We are particularly interrested in this problem where the input is positive and negative implicational basis of this context. Three results are presented: properties and rules are given to find mixte implications, the impossibility of generating a complete mixte implicational basis having just this data in general case and feasibility in case where context is considered reduced.Nous présentons dans cette thèse les définitions et notations liées aux systèmes de fermeture et montrons leur relation avec les théories de Horn. Nous nous intéressons ensuite à trois opérations sur les systèmes de fermeture : la borne supérieure, la borne inférieure et la différence. Nous proposons une caractérisation de ces différentes opérations selon la représentation des systèmes de fermeture que nous considérons. On s'intéresse ensuite au problème de génération d'une base d'implications mixtes d'un contexte formel. Nous étudions ce problème lorsque la donnée prise en considération est constituée des bases d'implications génériques positives et négatives de ce contexte. Trois résultats majeurs sont présentés : l'apport de propriétés et de règles d'inférence pour déduire des implications mixtes, l'impossibilité de générer une base d'implications mixtes juste et complète à partir de ces données dans le cas général, et la faisabilité dans le cas où le contexte est considéré réduit

Quelques aspects algorithmiques sur les systèmes de fermeture

Nous présentons dans cette thèse les définitions et notations liées aux systèmes de fermeture et montrons leur relation avec les théories de Horn. Nous nous intéressons ensuite à trois opérations sur les systèmes de fermeture : la borne supérieure, la borne inférieure et la différence. Nous proposons une caractérisation de ces différentes opérations selon la représentation des systèmes de fermeture que nous considérons. On s'intéresse ensuite au problème de génération d'une base d'implications mixtes d'un contexte formel. Nous étudions ce problème lorsque la donnée prise en considération est constitue e des bases d'implications génériques positives et négatives de ce contexte. Trois résultats majeurs sont présentés : l'apport de propriétés et de règles d'inférence pour déduire des implications mixtes, l'impossibilité de générer une base d'implications mixtes juste et complète à partir de ces données dans le cas général, et la faisabilité dans le cas où le contexte est considéré réduitCLERMONT FD-BCIU Sci.et Tech. (630142101) / SudocSudocFranceF

An Exhaustive Generation of Mixed and Purely Negative Implications from Purely Positive Ones.

International audienceThe objective of this article is to generate mixed implications based on only positive ones

Computing Implications with Negation from a Formal Context

International audienceThe objective of this article is to define an approach towards generating implicationswith (or without) negation when only a formal context K = (G, M, I) is provided. To that end, we define a two-step procedure which first (i) computes implications whose left-hand side is a key in the context K\tilde{K} representing the apposition of the context K and its complementary \tilde{K} with attributes in \tilde{M}(negative attributes), and then (ii) uses an inference axiom we have defined to produce the whole set of implications. The initial context K needs to be reduced

A new generic class of Frankl’s families

Frankl’s conjecture states that in a family of sets closed by union F such that F 6= {∅}, there is an element that belongs to at least half of the sets of F. There are several partial results of this conjecture. For example, it has been shown that families in which the smallest set is of size 1 or 2, or families closed both by union and by intersection are Frankl’s. In this article, by basing ourselves on an unseen recursive definition of the family of sets closed by union, we will define a new class of Frankl’s families. Subsequently, we will evaluate the size of this class for the first 6 values of n. Finally we will show that this class does not coincide with the already known Frankl’s classes